Question

Decide whether the experiment is a binomial experiment. Explain.

Selecting ten cards, one at a time with replacement and reshuffled from a standard deck of cards. The random variable is the number of blue cards obtained.

Condition 1:

Condition 2:

Condition 3:

Condition 4:

Answer 1

Condition 1: trials must be fixed. In given case total cards to be select 10. So this condition of fixed trial is satisfied

Condition 2: probability of success in each trial must be fixed or constant. In this case probability of selecting blue card will be same for each trial, because cards after drawing is replaced.

Condition 3: trials must be independent of each other. In this case selection of cards in every trial is independent of previous trials.

Condition 4: at each trial there must be only two possible outcomes. Success and failure. In given case selecting blue card is a success and selecting cards other than blue is considered as failure.

all conditions are satisfied so given experiment is binomial experiment.

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